Casimir energy and dilute dielectric ball

General formalism of quantum field theory and addition theorem for Bessel functions are applied to derive a formula for Casimir-Polder energy of interaction between a polarizable particle and a dilute dielectric ball. The equivalence of dipole-dipole interaction and the Casimir energy for dilute homogeneous dielectrics is proved on the basis of Lifshitz theory A novel method is proposed to derive the Casimir energy of a dilute dielectric ball without divergences in calculations, the average interatomic distance lambda serves as a physical cut-off. Different approaches to the calculation of the Casimir energy of a dielectric ball are reviewed.